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Proof step 596 from proof bitsand-cast (previous step)

sgn(mklist(false, n - 1) + false ' + true ' + bits) = false ' + true ' + bits, 2 + # bits = # bits1 ⊦ n = 0, lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits1, false ' + true ' + bits))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits2 + mklist(false, n - 1), bits3) + bitsand(false ' + true ' + bits, bits1))), bits3 + bits1 = [], bits3 = [], bits2 + mklist(false, n - 1) = []

User applied rule insert elim lemma

And obtained the following new goals

Proof step 597:
n = m + 1, sgn(mklist(false, m) + false ' + true ' + bits) = false ' + true ' + bits, 2 + # bits = # bits1 ⊦ n = 0, lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits1, false ' + true ' + bits))) = lastn(n + 1 + # bits, fillsgn(n + 1 + # bits, bitsand(bits2 + mklist(false, m), bits3) + bitsand(false ' + true ' + bits, bits1))), bits3 + bits1 = [], bits3 = [], bits2 + mklist(false, m) = []

Rule argument

seq: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1 subst: [n, m] → [n, m] rotate: T spec: nat inst: name: elim-pred-c

Additional information

Used simplifier rules: n ≠ 0 ⊦ m = n - 1 ↔ n = m + 1; (elim) Used terms: n, m